I've been looking high and low for a mathematical Book on String Theory. The only Book I could find was "A Mathematical Introduction to String Theory" by Albeverio, Jost, Paycha and Scarlatti. I only stumbled upon this because I really like Jost's other Books.

After reading it, I found myself craving more. However, the above book is extreemly short and doesn't cover alot sadly.

I've been having trouble reading the current textbooks on String Theory. To me it often seems that certain mathematical concepts are simply applied without checking or reasoning. Something that has been bugging me ever since studying QFT. As I'm not a physicist, it's rather likely that I'm still lacking the intuition to see these things.

My question is, are there any other Introductory Books/Review-Articles on String Theory written in a more mathematically rigorous way? By this I mean, books that are written in the style of a common Math book? ("Definition-Theorem-Proof-Style")

+1 Thanks, that book does indeed look very promising. I'll probably get this to review on QFT. Judging from the José's link however, the String Theory part doesn't seem to follow this rigor as was started in the QFT part. It seems to drift of into a the standard physics approach instead of a more mathematical one. @Jon, do you own a copy? Would you say this holds true for the printed version? I'll try getting my hands on one as soon as i can
–
Michael KissnerAug 2 '11 at 19:42

The published version differs significantly from the electronic notes. Here are the complete scans of both books: gen.lib.rus.ec/…
–
Dmitri PavlovAug 3 '11 at 9:01

There is the currently in-press book "Mathematical Foundations of Quantum Field and Perturbative String Theory" (n-cafe,nLab) edited by Schreiber and Sati and published in the AMS series Proceedings of Symposia in Pure Mathematics.

Links to arXiv copies of contributions are available at the above linked nLab page.

The mathematical aspects of string theory are wide-ranging, so I think looking for a mathematically rigorous treatment of the construction of string theories basically leads you to consider studying the output of a whole industry of mathematical physics research within algebraic geometry, representation theory, k-theory, differential topology, etc. There are a few mathematical books, e.g.:

I think rigorious string theory is just that what mathematicians make out of it when they got inspired.

If you had a course in classcial mechanics and have seen a Lagrangian and calculated a Gaussian integral once in your live you already know a lot about physics.

To get an insight into path integral calculations there is the great book "Mirror Symmetry" by Aspinwall, Klemm, Hori et al. It is split in physics and mathematics parts. (The mathematics does not define virtual fundamental class.)

Then there is the newer book called "Dirichlet branes and mirror symmetry". Here mathematics and physics are taught closer together.

A book on Gromow-Witten theory is "Mirror symmetry and algebraic geometry". It also contains an appendix expalaining Gauged Linear Sigma model, SCFTs etc. ()You find this stuff also in "Mirror Symmetry").